No and maybe.
You deduct property taxes that are allocated to the days you owned the home. You can't deduct taxes for a period you did not own the home.
On the sale on 12/19/19; suppose you paid tax on January 15, for the period 1/1-12/31. The buyer probably paid you a credit of 12 days of taxes as part of the closing. Even if they didn't, you can only deduct the tax amounts for when you owned the home. If your tax bill was paid in July for a 7/1-6/30 tax year, you would deduct less than half the amount, since you sold at about 5-1/2 months of ownership. And so on.
On the purchase dated 3/22/19, you again deduct taxes that are actually allocated for period you owned the home. If the seller prepaid a year's worth of tax in January, then you probably paid them a credit of about 8 months worth at closing. You can deduct those taxes as if you paid them directly to the town or county. You can also deduct them even if you didn't pay the seller. Then, if you paid another tax bill, you can also deduct that. For example, suppose taxes are due September for the tax year 7/1-6/30 (this is the case for NY school taxes, for example). At the closing, you paid a credit to the seller for about 3 months, through 6/30. Then you paid a full year to the taxing authority in September, you can deduct that entire amount as well.
If your property taxes are paid in arrears, as in Illinois, figuring the amount becomes more complicated, but the principle is the same. You deduct the taxes that are allocated to the period you owned the home only.
